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On this page are computer-accessible forms for the graph C4[ 72, 15 ] = PL(WH_12(2,0,1,5),[3^12,6^6]).

(I) Following is a form readable by MAGMA:

g:=Graph<72|{ {32, 40}, {36, 44}, {34, 40}, {36, 40}, {36, 41}, {34, 45}, {32, 48}, {33, 49}, {33, 53}, {34, 56}, {36, 56}, {33, 62}, {35, 60}, {26, 58}, {4, 37}, {16, 49}, {18, 48}, {30, 60}, {4, 39}, {16, 51}, {13, 46}, {9, 42}, {6, 37}, {21, 54}, {25, 58}, {1, 37}, {14, 42}, {10, 47}, {16, 53}, {11, 45}, {27, 61}, {26, 60}, {22, 48}, {24, 62}, {2, 37}, {12, 43}, {3, 43}, {5, 45}, {18, 58}, {20, 60}, {21, 61}, {7, 46}, {31, 54}, {30, 55}, {20, 61}, {12, 38}, {18, 56}, {1, 42}, {7, 44}, {10, 38}, {23, 59}, {30, 51}, {5, 43}, {31, 49}, {3, 44}, {17, 62}, {22, 57}, {28, 44}, {6, 55}, {14, 63}, {9, 56}, {7, 54}, {22, 39}, {5, 55}, {13, 63}, {8, 59}, {29, 46}, {1, 53}, {15, 59}, {13, 57}, {6, 50}, {3, 55}, {1, 52}, {31, 42}, {28, 41}, {26, 47}, {10, 63}, {6, 51}, {3, 54}, {19, 38}, {2, 52}, {31, 41}, {13, 59}, {12, 58}, {8, 62}, {4, 50}, {8, 63}, {25, 46}, {9, 48}, {11, 50}, {29, 39}, {15, 52}, {16, 43}, {9, 53}, {17, 45}, {19, 47}, {21, 41}, {4, 57}, {15, 50}, {18, 47}, {7, 57}, {22, 40}, {25, 39}, {2, 61}, {14, 49}, {12, 51}, {11, 52}, {25, 38}, {2, 66}, {11, 72}, {5, 67}, {8, 65}, {14, 68}, {15, 68}, {10, 68}, {17, 65}, {19, 67}, {23, 70}, {17, 67}, {21, 71}, {23, 68}, {27, 72}, {20, 64}, {20, 66}, {23, 64}, {27, 67}, {30, 70}, {24, 66}, {29, 71}, {28, 70}, {26, 64}, {19, 72}, {27, 71}, {28, 64}, {24, 69}, {24, 71}, {29, 66}, {32, 65}, {35, 65}, {33, 69}, {32, 69}, {35, 70}, {35, 69}, {34, 72} }>;

(II) A more general form is to represent the graph as the orbit of {32, 40} under the group generated by the following permutations:

a: (3, 8)(4, 11)(5, 13)(6, 15)(7, 17)(10, 12)(14, 16)(19, 25)(21, 24)(22, 34)(23, 30)(27, 29)(28, 35)(31, 33)(32, 36)(37, 52)(39, 72)(41, 69)(42, 53)(43, 63)(44, 65)(45, 57)(46, 67)(47, 58)(48, 56)(51, 68)(54, 62)(55, 59)(60, 64)(61, 66)
b: (1, 4, 11)(2, 6, 15)(3, 10, 24)(5, 14, 29)(7, 19, 33)(8, 21, 12)(9, 22, 34)(13, 27, 16)(17, 31, 25)(18, 32, 36)(20, 30, 23)(26, 35, 28)(37, 50, 52)(38, 62, 54)(39, 45, 42)(40, 56, 48)(41, 58, 65)(43, 63, 71)(44, 47, 69)(46, 67, 49)(51, 59, 61)(53, 57, 72)(55, 68, 66)(60, 70, 64)
c: (2, 9)(3, 13)(4, 31)(5, 8)(6, 14)(10, 30)(11, 33)(12, 23)(15, 16)(18, 20)(19, 35)(21, 22)(24, 34)(25, 28)(27, 32)(29, 36)(37, 42)(38, 70)(39, 41)(40, 71)(43, 59)(44, 46)(45, 62)(47, 60)(48, 61)(49, 50)(51, 68)(52, 53)(54, 57)(55, 63)(56, 66)(58, 64)(65, 67)(69, 72)
d: (1, 3, 26, 8)(2, 7, 18, 17)(4, 36, 19, 24)(5, 20, 13, 9)(6, 28, 10, 33)(11, 21, 25, 32)(12, 35, 15, 31)(14, 16, 30, 23)(22, 34, 27, 29)(37, 44, 47, 62)(38, 69, 50, 41)(39, 40, 72, 71)(42, 43, 60, 59)(45, 61, 46, 48)(49, 51, 70, 68)(52, 54, 58, 65)(53, 55, 64, 63)(56, 67, 66, 57)
e: (1, 2, 20, 26, 18, 9)(3, 5, 17, 8, 13, 7)(4, 21, 30, 19, 32, 14)(6, 27, 35, 10, 22, 31)(11, 24, 23, 25, 36, 16)(12, 34, 33, 15, 29, 28)(37, 61, 60, 47, 48, 42)(38, 40, 49, 50, 71, 70)(39, 41, 51, 72, 69, 68)(43, 45, 62, 59, 46, 44)(52, 66, 64, 58, 56, 53)(54, 55, 67, 65, 63, 57)

(III) Last is Groups&Graphs. Copy everything between (not including) the lines of asterisks into a plain text file and save it as "graph.txt". Then launch G&G (Groups&Graphs) and select Read Text from the File menu.

**************

&Graph
C4[ 72, 15 ]
72
-1 37 52 42 53
-2 66 37 61 52
-3 44 55 43 54
-4 57 37 39 50
-5 55 45 67 43
-6 55 37 50 51
-7 44 46 57 54
-8 59 62 63 65
-9 56 48 42 53
-10 68 47 38 63
-11 45 50 72 52
-12 58 38 51 43
-13 46 57 59 63
-14 68 49 63 42
-15 68 59 50 52
-16 49 51 53 43
-17 45 67 62 65
-18 56 47 58 48
-19 67 47 38 72
-20 66 60 61 64
-21 71 61 41 54
-22 57 48 39 40
-23 68 59 70 64
-24 66 69 71 62
-25 46 58 38 39
-26 47 58 60 64
-27 67 71 61 72
-28 44 70 41 64
-29 66 46 71 39
-30 55 70 60 51
-31 49 41 42 54
-32 69 48 40 65
-33 69 49 62 53
-34 45 56 72 40
-35 69 70 60 65
-36 44 56 40 41
-37 1 2 4 6
-38 12 25 19 10
-39 22 25 4 29
-40 22 34 36 32
-41 36 28 31 21
-42 1 14 9 31
-43 12 3 5 16
-44 3 36 28 7
-45 11 34 5 17
-46 13 25 7 29
-47 26 18 19 10
-48 22 18 9 32
-49 33 14 16 31
-50 11 4 15 6
-51 12 16 6 30
-52 11 1 2 15
-53 33 1 16 9
-54 3 7 31 21
-55 3 5 6 30
-56 34 36 18 9
-57 22 13 4 7
-58 12 25 26 18
-59 23 13 15 8
-60 35 26 30 20
-61 2 27 20 21
-62 33 24 17 8
-63 13 14 8 10
-64 23 26 28 20
-65 35 17 8 32
-66 2 24 29 20
-67 5 27 17 19
-68 23 14 15 10
-69 33 24 35 32
-70 23 35 28 30
-71 24 27 29 21
-72 11 34 27 19
0

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